Proth Search Page |

Primes k · 2 + 1 ^{n} |
List of primes for k < 300
List of primes for 300 < k < 600
List of primes for 600 < k < 900
List of primes for 900 < k < 1200
Frequencies (draft) History (under preparation) |

Fermat numbers |
Standard factoring status
Factors of generalized Fermat numbers GFN03 factoring status GFN05 factoring status GFN06 factoring status GFN07 factoring status GFN10 factoring status GFN11 factoring status GFN12 factoring status Search limits and reservations |

Primes k · 2 − 1 ^{n} |
List of primes for k < 300 |

The Sierpiński problem |
Definition and status |

The Riesel problem |
Definition and status |

Cullen primes |
Definition and status |

Woodall primes |
Definition and status |

New factorization at GFNsmall.html:

Cofactor of 10^(2^8) + 3^(2^8) is P85 × P105.

January 25, 2020:

Lists of primes

all currently known primes included.

January 22, 2020:

New factor of Fermat number F(5523858):

Same factor also divides Generalized Fermat numbers

GF(5523856,11), xGF(5523857,9,5), xGF(5523858,10,9),

xGF(5523858,11,2), xGF(5523857,11,4), xGF(5523858,11,8).

GFNfacs.html now includes 6653 new divisibilities.

Number of divisibilities discovered in previous years:

39 (2019), 21 (2018), 18 (2017) 42 (2016), 78 (2015).

December 25, 2019:

December 9, 2019:

New factor of Fermat number F(2587), which brings to 350

the total number of known factors.

October 16, 2019:

New factors of Generalized Fermat numbers GF(4800313,3)

and GF(4800310,5).

October 14, 2019:

New factor of Generalized Fermat number GF(4673541,7).

October 13, 2019:

New factor of Generalized Fermat number GF(4532462,11).

September 29, 2019:

New factor of Generalized Fermat number GF(3964696,11).

July 31, 2019:

Generalized Fermat number GF(25,10) proved composite.

July 6, 2019:

Generalized Fermat number GF(24,10) proved composite.

March 23, 2019:

New factor of Fermat number F(9863).

January 28, 2019:

New factor of Fermat number F(118).

December 31, 2018:

Table of factors GFNfacs.html now includes 6608

new divisibilities, 21 of them found in 2018.

December 19, 2018:

New factor of Fermat number F(132).

December 13, 2018:

New factor of Fermat number F(3345).

November 2, 2018:

New factor of Fermat number F(2144).

July 24, 2018:

New factor of Fermat number F(5199), which brings to 300

the total number of known composite Fermat numbers.

May 1, 2018:

New factor of Generalized Fermat number GF(10746,12).

April 5, 2018:

New factor of Fermat number F(274).

April 3, 2018:

Candidate of Extended Sierpinski Problem eliminated.

March 10, 2018:

New factor of Fermat number F(63480).

January 15, 2018:

New factorization at GFNsmall.html:

Cofactor of 11^(2^8) + 10^(2^8) is P62 × P107 .

December 30, 2017:

Riesel problem candidate eliminated!